Starting by two–photon absorption, a process which was discussed in–depth by Henriques et al. [1]}, we perform the necessary calculations with a broadening small enough such that the resonance associated with each individual intra–excitonic energy level transition can be clearly identifiable \(\left( \Delta =0.05\,\mathrm {meV}\right)\) . The two–photon absorption third–order susceptibility is then normalized by the value at the \(E_{1s\rightarrow 3d}\)  resonance as to facilitate the comparison of each peak. Of note is the amplitude of the resonance associated with the \(E_{1s\rightarrow 7d}\)  transition, peaking at around \(40\%\)  of the maximum.
